Imprecise uncertainties in design and decision making---Propagation and effects

Modeling uncertainty through probabilistic representation in engineering design is common and important to decision making that considers risk. However, representations of uncertainty often ignore elements of "imprecision" that may limit the robustness of decisions. Further, current approaches that incorporate imprecision suffer from computational expense and relatively high solution error. This work presents the Computational Efficient Imprecise Uncertainty Propagation (CEIUP) method which draws on existing approaches for propagation of imprecision and integrates sparse grid numerical integration to provide computational efficiency and low solution error for uncertainty propagation. The first part of the thesis details the methodology and demonstrates improvements in both computational efficiency and solution accuracy as compared to the Optimized Parameter Sampling (OPS) approach for a set of case studies. The second half of the thesis is focused on estimation of non-dominated design parameter spaces using decision policies of Interval Dominance and Maximality Criterion in the context of set-based sequential design-decision making. A gear box design is presented and compared with OPS, demonstrating that CEIUP provides improved estimates of the non-dominated parameter range with faster solution times. The third part of the thesis focuses on the effect of risk attitudes, risk towards innovation and imprecision in making choice by considering elements of Choice Theory. Also a framework has been proposed in the third part for concept selection consider risk attitudes, risk towards innovation and imprecision. Various scenarios of a gearbox design problem have been used for the study in the third part of this work. The work concludes with an overview of design problem scenarios in which CEIUP is the preferred method and offers opportunities for extending the method.